PH Y S- 12 00 11
Section_ _ __
-----------
25 0 La b M an ua l
Name
h Length
35 A - T w o B ea m Interference - Pat
and polarization,
(/0), frequency (co)
ity
ns
te
in
e
m
sa
e
ith th
m ag ne tic waves w
is:
W he n tw o el ec tro
e resultant intensity
th
,
nt
incide
co
e
ar
e,
as
ph
t
en
er
bu t di ff
Eq. 35a
2
I= 4 /0 cos (
e which
ch wave has a phas
Ea
.
es
av
w
o
tw
e
th
een
n, and
as e difference betw
and index), reflectio
e
nc
ta
is
(d
w he re Ll ¢ is the ph
th
ng
le
tical pa th
ef fe ct s, including op
de pe nd s on various ce,
eren
or ig in al ph as e diff
Eq. 35b
2t r
A + ~ ¢rejlectionA
)
nL
rig ina /A +
~¢]
¢A
T ~(
= ¢o
V
ohase difference du
W e focus here on
/
C
!:J.(nl)
e to oath difference
•, >
_\
.,t 'tf _'
·
, (- ;,lO)
'I(
.
I D :)
-
\
th A=500 nm
beam has wave leng
ch
Ea
e.
ac
rf
su
a
on
ought together
e fo llo w in g path
ams of lig ht are br
nsity fo r ea ch of th
te
in
nt
lta
su
re
e
th
1) T w o pa ra lle l be
What is
2
lm at the surface.
an d in te ns ity I W
the beams?
ff er en ce s between
di
e
as
ph
or
s
th
ng
le
2
Intensity (W lm )
th di ff er en ce
Ph as e or pa th le ng
'-\
0 ra di an s (p ha se )
bO O" ' I O Ci_,1
)
n/ 2 ra di an s (p ha se
.:?_
)
60 de gr ee s (p ha se
3
0
,
"r( y-- ,
1 ,,q1,
l-(' ~ 1(( It~ ~ ~
L/
Lf /0, r 4 rd. , ---
)
3n ra di an s (p ha se
\
th )
30 0 nm (p at h le ng
th )
10 00 ru n (p at h le ng
l( ,( (,b~ .
)
5 .5 1v (p at h le ng th
(l"
ilA,l , ts
. fl /~ L
'
s
... q :w , 2/ I l 0.) :. I01 2
-1,,
separated by
two points in space
n
ee
tw
be
e
lin
ht
ig
ls al on g a stra
th )._ trave
ng
le
e
av
w
f
.
2) A w av e o
~
ts.
m
po
o
tw
e
es
ave at th
w
di st an ce L.
e
th
in
ce
en
er
ff
e di
~ '\\ L
a) Fi nd th e ph as
)
efJ
r
1- 11 L
~
i\
ra di an s
,..,,.-=--
1
121
PHYS-1200/1250 Lab Manual
Section_ _
Name:_ _ _ _ _ _ _ __
b) A wave (A) with vacuum wavelength of Av travels a
distance of L1 in a medium with index of refraction
n 1, then distance L2 in a medium with index ni , then a
distance fa in a medium of index n1. Fill in the table
to the right with the change in phase for the wave
traveling through each of these regions.
LI
~
D1
Distance
for wave
A
Index
for A
L1
n1
Phase change in
region for A
'l1r l" 1-IJ LI
?---
1
'I
n2
L2
2-~ ( n ~ - l) L'\_
?--
I
l
r
n1
7-.,-- LV)'\> - l ) L:,
?<-
I
c) For wave A, what is the total change in phase from the start to the end of this path (in terms of
distances, vacuum wavelength, and indexes of refraction)?
l_\i_
l
· L-, 1 • Y\1
ILL,
.\--
'~
)
L1. ''r. 1, -t LJ h \ -{t.- 1 ., c i'·+-LJ) _____radians
-
d) Light wave B travels the same physical distances as
beam A, but the index in one of the regions is
different (L2, m). Fill in the phase change in the table
to the right for this case.
Distance
forB
Index
forB
L1
Phase change
in region for B
n1
1.1\(v-11- I ) ~
1
7-,
L2·
n3
"2 7
/
l r1 3-I) Li
'A
L3
-
n1
71T (".',, - 1) L-3
7\,,
e) In an interferometer, a single beam can be split so that part of it travels path A as above and the
other travels path B. What is the difference in phase between these two beams in terms of (L;, n; ,
~
and k)?
\Lc·~rl- ~L-r, J
f)
On which of the following variables does the phase difference between the two beams depend?
(Circle all ~
cf:li _
ppiy:-)
L2
~
L3
n1
I
n2~
:s
A.v
j
g) Some of the variables above don't matter. Explain which ones and why you thi
L,
L2
L3
n1
n2
n3
IA V\ ~
<-
CAP pl elf
'w-1 (
A
lvt.~\~h
IV'\
122
V, cl-{iln
~
t-
PHYS-12 00/1250 Lab Manual
Name_ _ _ _ _ _ _ _ __
Section,_ _ __
3) A beam of light of vacuum wavelength A.vac = 600 .00 run is split into two beams.
• Beam I travels the following lengths through the respective mediums:
AIR
GLASS
VACUUM
GLASS
Lair - 10 cm
L lass - 1 mm
Lvac - 1 mm
L lass = 1 mm
• Beam II travels the following lengths through the respective mediums:
AIR
GLASS
AIR
GLASS
Lair= 10 cm
L lass= 1 mm
Lvac = 1 mm
L1ass=lm m
AIR
Lair = 10 cm
AIR
Lair= 10 cm
The index of refraction for each medium is:
Dair= r.0003, Ilglass = 1.5000, nvacuum = 1.0000
a) Find the phase difference between
these two beams at the end of their
paths.
~,~\~ ~~
\\\_\\
-:. \ \"/\ ~\~ \\ IJ, ,
t.. ~ ~ \ li\V"\ \
_
\
l
\.
IM1\ \ \\,, \
Mirror A
✓
L:w,
\, \) \) ~ 'l ..... \,w o'\
L..,
Screen
t!
Lg1,m
l l
·p h 1rft
()Jf~ tl\.l (
(~
' (_:~
'I )f l o-7
\
Mirror B
L,,;,.
V 'C_vt't.!k /J-'1 /
Semi Silv=d
b) As~g each of the beams has power
of -1v{~~nd the power of the combined
beams.
\r\¼11..<.\-\
Beam Sp
Source
)_ _t Jfl
!L +- 1~
INTER FEROM ETER DIAGR AM
- . ~r t1 LC\ ~ \
(,o \
\l
r;"'\- ~
1...
-
'l
j: eu.. ,_1.r, .~
-I
- 11
co
)
::. o
~l.
123
PHYS-12OO/125O Lab Manual
Name
----- -----
Section_ _ __
35B - Experiment: Two Slit Interference
Equipment: Pasco magnetic optical rail; Red semiconductor laser diode; diode power
supply; Pasco Multiple Slit mask; a white screen to view the interference pattern; a small
ruler to measure distance on the interference image.
Background: If waves with the same wavelength emanate from two points and travel in straight paths (rt
and r2) through a uniform material (index n) to a common point as shown to the right, they will be out of
phase according to:
21m('i - ri) (
/:J.¢ ---'----=- + 'P;1 A,v
d
'P; 2 ) . If r1 and r2 are very large compared to the distance between the sources ,
. then ( 1j - r2 ) ;:;; d sin 0 where 0 is the angle between the normal to a line from one source to the other and
a line from sources to measurement point. This is shown schematically in the lower sketch above. If also
the original phases
.
(
</J; 1
,1.
and </J; 2 ) for the two sources are the same, /:J.'f
h"b.
.
21mdsin0
, which ex 1 its a
2
V
maximum in intensity whenever /:J.¢ is an integer (m) multiple of 2;., or when mAv = nd sin0m.
Top View'
Screen _
i
d
y
~~.(..¥~& 4-+-r+++ +H _J_
a subscript v.
. t f labeling the wavelength
. with
1) We made a porn o
think .2 with this subscnpt denotes?
a) What do you
J -~
\j\,~~~l"t\.
.
1\1\
\)~ \}.,~¼-
A,v
b) Describe the meanmg of -;; ·
~~ \ft\ \l l\\_ \,\,\}\'\
·rt~n,..c.~~~
124
CZ
PHYS-1200/1250 Lab M
anua1
Name
--------
2) Record the infonnation for th
e pattem you observe in the table b
d(mm)
D (nun)
(from the mask)
Q 25
(measured using
meter stick)
O,J
~
~
CJ
~
(chosen by you)
7 ~() .
-3
~Y
1
1,0
Section,_ _ __
elow.
A
= Yright - Yleft
(observed on the
screen)
(Calculated from
the other
information in the
table)
\S '1-\ lY\
'--{
\D l'ln"Vl
oJ
7?◊
0.50
Io
L0l
0.50
lq
I
0.50
b
'7 0~
A-
=
A."tvi
b
6
/J IJ _~ n ~ ,d ,
A. v
-0
_
,.. , 0
h _ 7 t;7
t'h_ Wj
~
-b
""'
-lo M
tu -7 .,___
. . , ,v -7 h-,
7 _1 b 1. 2.7 " / u - 7
[., . () n \ ,vi
1
I - bO
<o • S.2: ...
'i? - O"hwi
~
?<. ID
\ . l>"-10
1i?~W\
i
_1,,
\ ~ lo
•
3) Calculate.'.}the waveJf the laser using th6\'ilfo£at~n1 n your .table and record it in the table.
Calculate the average wavelength from your measurements.
Average Wavelength: __b_.·_7_
7
_ __
i-°"'"
,.._ 1_0_ ~ _ _.:_
4 ) Compare your measurement to the typical wavelength range for red light? (You can check the text or
or t foogle ™ it, but indicate your source.)
Bi~
~
, - ·: ; : "· ~ . \
~
1\_.. l,\., 'ti Yt\.6- V\ •
\)h-"1 v"rtl<
o
eclV\, •
J'
5) you should have noticed that the width o~ the
n the screen that you could see bnght
.
·t
h ·
region o
.vely narrow. T e mtens1 y
d
.
spots on was re1atI
thing like this. Why o you
pattern lookedalslom:em drops in intensity to the
think the over pa
sides?
Ture l~
l
Oi\
J
c..v1.q Q,
J
-2
0
2
------,
4
6
126
Name._ _ _ _ _ _ _ _ _ _ __
PHYS-1 200/125 0 Lab Manual
Sect ion-- --
ce peaks
3SD - t·The. Diffract· ion Grating
. . rfi
Ob·
eren
mte
g
observm
by
grating
n
diffractio
a
of
lines
between
spacing
the
e
~~c ive. Determm
th
.
eng
wavel
for hght of a specific
Equipment: Low power laser. Diffraction grating, PASCO magnetic optics rail, PASCO
magneti c optics carrier, Black metal safety screen, Ruler.
II
_LASER SAFETY: Avoid shining the laser in these laboratories directly into anyone' s
. eyes. Prolonge d direct viewing of the beam can lead to permane nt eye damage .
-
th
periodic
Background: A diffraction grating consists of a reflective or transmitting surface wif a acts as a
In h ·
f li
array O nes. t e simplest theoretical model, we assume that each line on the gra mg th nd
g ath
infinites imally thin emission source with all of the sources emitting at the same wavelen
of e
in set phase to one another. For a beam of wavelength "- at normal incidenc e to the plane
grating, interfere nce peaks will be observed at angles
em= arcsin( :)., J,where mis an integer
- (Order of Interference) and dis the distance between the grating emitting lines .
Scree n
51 /\
1.,( 0.3 .:.
l:,,s o ,,< 10·"1
::..--- -
y-
d,
)
y+
cL =
1
•
Lase r Apparatus
,I ,
on a magnet ic
Procedure: Set up the laser so that it shines through the middle of a grating held in place
two interfer ence
carrier. Measure the lateral displacement between the central maximu m peak and the
the grating to
from
maxima on either side of it. Record this measurement and the distance D of the ruler
therefor e the
the screen to compute the angle. (The angle may be large - greater than 20 degrees -
viewing ruler may have io be close to the grating.)
and comput e the
Make at least 4 measurements with different D's. Use a laser wavelen gth "- = 650 nm
d-spacin g for each measurement.
D (mm)
TRIALS
1
LS 5
2
7 "
4
)--)...U
l
d
'I - 1
I
ni::
J
'f1
l,d
l>
40
·4
b
C,,7. )d o-7
,
c ,I\
e
\(
Jl
._
-
_1:,
,-,,,
l(J
7'-
10-
~
)
A')
b «· C>I lf!Q( rom st~dard deviatio n of your 8 me
Average d-spacin g= ~,~I "'1•- +/nts
asureme
n.
er
centimet
per
Imes
Gratings are often descnbe d 1~ terms of th~ number of
I O\..I
Convert your d-spacing into Imes per centimeter.
k..
-=- lt c;u I'\ M
':6...
IA -:-
1e
l..(S D
LI ~
3
i}-- os-0
d+
I
>,
-
'b' ""
±d. -
---..:_=-- /
loQ O6' i,11
l
130